On H -Valued Continuous Robbins - Monro processes. By: Hoda Mohamed Ali and Hala Elnagar. | ||
| The Egyptian Statistical Journal | ||
| Article 1, Volume 42, Issue 2, December 1998, Pages 155-164 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1998.314572 | ||
| Abstract | ||
| In this work, we consider a continuous Robbins - Monro process in a Hilbert space, a nonlinear mapping ƒ is treated instead of the usual linearity assumption. A modified process with varying truncations is analyzed, and the asymptotic properties are investigated and convergence as well as necessary and sufficient conditions are obtained. Yin and Zhu [7] considered the discrete Robbins Monro in a Hilbert space, and we extend their results to the continuous case, by introducing randomly varying truncations and we prove the almost sure convergence of the stochastic approximation algorithms. | ||
| Keywords | ||
| Almost Sure Convergence; Continuous Robbins-Monro Process; Hilbert Space; Modified Process; Nonlinear Mapping; Stochastic Approximation Algorithms | ||
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